[Genrp] Fwd: FOM "weighted" vs "unweighted" examples from GEp-III/GEp-2gamma

[Michael Kohl]

Dear all,

I am sharing here Andrew’s follow-up message with the mailing list as this is very useful information.

Thank you Andrew!

—Michael


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Dr. Michael Kohl
Interim Chair
Joint Professor and Staff Research Scientist
Physics Department, Hampton University, Hampton, VA 23668, USA
Jefferson Lab, 12000 Jefferson Avenue, Newport News, VA 23606, USA
Phone: +1-757-727-5153 (HU office)
Email: kohlm at jlab.org<mailto:kohlm at jlab.org>
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Begin forwarded message:

From: Andrew Puckett <puckett at jlab.org<mailto:puckett at jlab.org>>
Subject: FOM "weighted" vs "unweighted" examples from GEp-III/GEp-2gamma
Date: December 4, 2025 at 1:32:25 PM EST
To: Michael Kohl <kohlm at jlab.org<mailto:kohlm at jlab.org>>

Following up today’s meeting discussion:

https://inspirehep.net/literature/1613323

Focus on Figs. 9,10, Table V, Fig. 12, and Table XI.  The main variables on which the asymmetry depends are the polar scattering angle in the FPP and the spin precession variation within the acceptance.

We should focus on the 2.5 GeV^2 and 8.5 GeV^2 kinematics, since these have precession angles close to 90 deg (270 deg) respectively, so the effect of spin precession on the acceptance-averaged azimuthal asymmetry is minimal.

The acceptance-averaged focal-plane asymmetries are shown in Tab. V, with all events passing all the selection criteria.

The ratio c/s is a proxy for PT/PL which is a proxy for GE/GM. If I take the weighted average of FPP1 and FPP2 asymmetries in Tab. V for, e.g., the high-epsilon, 2.5 GeV^2, and then form the ratio, the implied relative statistical uncertainty in the FF ratio is about 1.03%.

On the other hand, if I go to Table XI, the fractional uncertainty in the final FF ratio from the unbinned ML extraction is 0.85%.

So the effect of weighting events by analyzing power (parametrization and distribution shown in Fig. 14 and Tab. VII) and spin transport matrix elements event-by-event (see e.g. Fig. 12) for this kinematics is about a 17% reduction of the error bar.

The reduction for 5.2 GeV^2 is obviously much bigger.

In SBS the spin precession angle (for protons anyway) is roughly constant within the acceptance (not sure about neutron precession). So the main effect will be the Ay variation within the acceptance. If the Ay distribution is constant, then there would be effectively no difference in FOM between an unbinned ML extraction and extracting the acceptance-average azimuthal asymmetry a la Tab. V and Figs. 9,10.

Cheers,
Andrew




Andrew Puckett
Professor, Physics Department
University of Connecticut
196 Auditorium Road, Unit 3046
Storrs, CT 06269-3046
Office phone: (860) 486-7137
https://puckett.physics.uconn.edu<https://puckett.physics.uconn.edu/>
puckett at jlab.org<mailto:andrew.puckett at uconn.edu>

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